On the connection between the pinch technique and the background field method

The connection between the pinch technique and the background field method is further explored. We show by explicit calculations that the application of the pinch technique in the framework of the background field method gives rise to exactly the same results as in the linear renormalizable gauges. The general method for extending the pinch technique to the case of Green's functions with off-shell fermions as incoming particles is presented. As an example, the one-loop gauge independent quark self-energy is constructed. We briefly discuss the possibility that the gluonic Green's functions, obtained by either method, correspond to physical quantities.Comment: 13 pages and 3 figures, all included in a uuencoded file, to appear in Physical Review

The heavy quark decomposition of the S-matrix and its relation to the pinch technique

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0

Electroweak pinch technique to all orders

The generalization of the pinch technique to all orders in the electroweak sector of the Standard Model within the class of the renormalizable 't Hooft gauges, is presented. In particular, both the all-order PT gauge-boson-- and scalar--fermions vertices, as well as the diagonal and mixed gauge-boson and scalar self-energies are explicitly constructed. This is achieved through the generalization to the Standard Model of the procedure recently applied to the QCD case, which consist of two steps: (i) the identification of special Green's functions, which serve as a common kernel to all self-energy and vertex diagrams, and (ii) the study of the (on-shell) Slavnov-Taylor identities they satisfy. It is then shown that the ghost, scalar and scalar--gauge-boson Green's functions appearing in these identities capture precisely the result of the pinching action at arbitrary order. It turns out that the aforementioned Green's functions play a crucial role, their net effect being the non-trivial modification of the ghost, scalar and scalar--gauge-boson diagrams of the gauge-boson-- or scalar--fermions vertex we have started from, in such a way as to dynamically generate the characteristic ghost and scalar sector of the background field method. The pinch technique gauge-boson and scalar self-energies are also explicitly constructed by resorting to the method of the background-quantum identities.Comment: 48 pages, 8 figures; v2: typos correcte

Tau anomalous magnetic moment form factor at Super B/Flavor factories

The proposed high-luminosity B/Flavor factories offer new opportunities for the improved determination of the fundamental physical parameters of standard heavy leptons. Compared to the electron or the muon case, the magnetic properties of the $\tau$ lepton are largely unexplored. We show that the electromagnetic properties of the $\tau$, and in particular its magnetic form factor, may be measured competitively in these facilities, using unpolarized or polarized electron beams. Various observables of the $\tau$'s produced on top of the $\Upsilon$ resonances, such as cross-section and normal polarization for unpolarized electrons or longitudinal and transverse asymmetries for polarized beams, can be combined in order to increase the sensitivity on the magnetic moment form factor. In the case of polarized electrons, we identify a special combination of transverse and longitudinal $\tau$ polarizations able to disentangle this anomalous magnetic form factor from both the charge form factor and the interference with the Z-mediating amplitude. For an integrated luminosity of $15 \times 10^{18} b^{-1}$ one could achieve a sensitivity of about $10^{-6}$, which is several orders of magnitude below any other existing high- or low-energy bound on the magnetic moment. Thus one may obtain a QED test of this fundamental quantity to a few % precision.Comment: 20 pages, 4 figure

Strangeness contribution to the vector and axial form factors of the nucleon

The strangeness contribution to the vector and axial form factors of the nucleon is presented for momentum transfers in the range $0.45<Q^2<1.0$ GeV$^2$. The results are obtained via a combined analysis of forward-scattering parity-violating elastic $\vec{e}p$ asymmetry data from the $G^0$ and HAPPEx experiments at Jefferson Lab, and elastic $\nu p$ and $\bar{\nu} p$ scattering data from Experiment 734 at Brookhaven National Laboratory. The parity-violating asymmetries measured in elastic $\vec{e}p$ scattering at forward angles establish a relationship between the strange vector form factors $G_E^s$ and $G_M^s$, with little sensitivity to the strange axial form factor $G_A^s$. On the other hand, elastic neutrino scattering at low $Q^2$ is dominated by the axial form factor, with still some significant sensitivity to the vector form factors as well. The combination of the two data sets allows the simultaneous extraction of $G_E^s$, $G_M^s$, and $G_A^s$ over a significant range of $Q^2$ for the very first time.Comment: 3 pages, 1 figure, will appear in AIP Conference Proceedings for PANIC 200

Radiative Corrections to W and Quark Propagators in the Resonance Region

We discuss radiative corrections to W and quark propagators in the resonance region, |s-M^2| \lsim M*Gamma. We show that conventional mass renormalization, when applied to photonic or gluonic corrections, leads in next to leading order (NLO) to contributions proportional to [M*Gamma/(s-M^2)]^n, (n=1,2...), i.e. to a non-convergent series in the resonance region, a difficulty that affects all unstable particles coupled to massless quanta. A solution of this problem, based on the concepts of pole mass and width, is presented. It elucidates the issue of renormalization of amplitudes involving unstable particles and automatically circumvents the problem of apparent on-shell singularities. The roles of the Fried-Yennie gauge and the Pinch Technique prescription are discussed. Because of special properties of the photonic and gluonic contributions, and in contrast with the Z case, the gauge dependence of the conventional on-shell definition of mass is unbounded in NLO. The evaluations of the width in the conventional and pole formulations are compared and shown to agree in NLO but not beyond.Comment: 19 pages, 7 figures, LaTeX (uses epsfig). Slight rewording of the abstract and one of the sentences of the text. Minor misprints corrected. To appear in Phys. Rev.

The Two-Loop Pinch Technique in the Electroweak Sector

The generalization of the two-loop Pinch Technique to the Electroweak Sector of the Standard Model is presented. We restrict ourselves to the case of conserved external currents, and provide a detailed analysis of both the charged and neutral sectors. The crucial ingredient for this construction is the identification of the parts discarded during the pinching procedure with well-defined contributions to the Slavnov-Taylor identity satisfied by the off-shell one-loop gauge-boson vertices; the latter are nested inside the conventional two-loop self-energies. It is shown by resorting to a set of powerful identities that the two-loop effective Pinch Technique self-energies coincide with the corresponding ones computed in the Background Feynman gauge. The aforementioned identities are derived in the context of the Batalin-Vilkovisky formalism, a fact which enables the individual treatment of the self-energies of the photon and the $Z$-boson. Some possible phenomenological applications are briefly discussed.Comment: 50 pages, uses axodra

Asymptotic properties of Born-improved amplitudes with gauge bosons in the final state

For processes with gauge bosons in the final state we show how to continuously connect with a single Born-improved amplitude the resonant region, where resummation effects are important, with the asymptotic region far away from the resonance, where the amplitude must reduce to its tree-level form. While doing so all known field-theoretical constraints are respected, most notably gauge-invariance, unitarity and the equivalence theorem. The calculations presented are based on the process $f\bar{f}\to ZZ$, mediated by a possibly resonant Higgs boson; this process captures all the essential features, and can serve as a prototype for a variety of similar calculations. By virtue of massive cancellations the resulting closed expressions for the differential and total cross-sections are particularly compact.Comment: 23 pages, Latex, 4 Figures, uses axodra